Complex Transfer Function Research Articles

Dual‐port network‐based impedance modelling and AC‐port characteristic analysis of wound rotor synchronous machine for more electric aircraft

AbstractDue to the increasing variety of converters in more electric aircraft (MEA), the stability of the MEA power system has become a critical issue that receives wide concerns. As the primary power source for MEA, the wound rotor synchronous machine (WRSM) greatly affects the stability of the whole power system, and therefore accurate modelling of the WRSM serves as the basis for the analysis of system characteristics and even stability. Nevertheless, the complex structure and coupling of WRSM bring great challenges to small‐signal modelling methods. This paper introduces a novel method to model the WRSM in a modular and cascaded manner. Instead of deriving the complex transfer function, the proposed method uses a dual port to model each component. By connecting the dual port of each component from the rear stage to the front stage in a cascaded way, a dual‐port network can be built to describe the external impedance characteristics of the WRSM. Kirchhoff law can be applied to calculate the impedance by circumventing the complicated decoupling process. The proposed dual‐port network model has been validated on a hardware‐in‐loop platform. Furthermore, the output impedance characteristics of the AC port has also been analysed with the proposed model.

ECONOMIC AND MATHEMATICAL MODELING OF THE RENEWABLE ENERGY DEVELOPMENT IN UKRAINE

Objective. The objective of the article is to apply economic and mathematical models for the analysis, modeling and forecasting of the development of renewable energy in Ukraine, assessment of country's renewable energy sources potential. Methods. The following methods are used to model and forecast the development of renewable energy in Ukraine: correlational and actocorrelational analysis (to identify the relationship between macroeconomic indicators of Ukraine and the development of renewable energy in the country); three-factor autoregressive and multiplicative forecasting and five-factor regression forecasting (for forecasting indicators of renewable energy of Ukraine); the basics of the mathematical apparatus for the analysis of transient processes, the methodology of determining the coefficients of impulse-transient and transient functions, methods of building differential models, Laplace transformation and obtaining transient functions, the basics of the mathematics of imaginary quantities, methods of obtaining the amplitude-phase and frequency characteristics of the object under study, methods of analysis stability of controlled dynamic processes (to present the Total renewable energy indicator in the form of a dynamic transient process and model its future states by obtaining a second-order differential equation with a simple input, a complex transfer function and by determining the amplitude-phase frequency characteristic and constructing a Nyquist frequency hodograph, which showed the stability of the studied process to external disturbances). Results. Forecasting the installed capacities and production volumes of renewable energy is an important task for the effective development of this industry. A new approach to forecasting is proposed, combining autoregressive and multivariate regression models and dynamic modeling. The development of the capacity of renewable energy is considered as a dynamic transient process, which is represented by a complex transfer function with its real frequency characteristic and its imaginary frequency characteristic, which are used to construct the Nyquist hodograph, which shows the stability of the researched process of development of the capacity of renewable energy from investment investments. According to the results of modeling based on the transient process method, a model of changes in the volume of installed capacities of renewable energy of Ukraine depending on the volume of investments in renewable energy is obtained in the form of a differential equation, and it is found out that this process is stable, that is, even with temporary restrictions or reductions of such investment over time it will return to a stable growing trend. The proposed method of dynamic modeling makes it possible to obtain more accurate and reliable forecasts of the development of renewable energy capacity, compared to traditional methods. This method can be used to make informed decisions regarding the development of solar energy and investment in this industry in Ukraine.

Impact of Soil Moisture Dynamics and Precipitation Pattern on UK Urban Pluvial Flood Hazards Under Climate Change

AbstractThe diversity of flood‐generating mechanisms superimposed on catchment physiographic features with non‐stationary meteorological drivers makes future flood hazard assessment a grand challenge. To date, many studies have examined patterns in rainfall and streamflow, but far fewer have investigated trends in the other drivers of flooding. The complex transfer function between precipitation and flooding makes it potentially misleading to simply look at the change in rainfall to express the hazard. Furthermore, there are very few studies that have directly used output from km‐scale climate models in flood modeling. Coarse resolution climate data sets may not credibly resolve local climate and weather extremes. Changes in rainfall distribution and antecedent moisture over extended time periods due to climate change have so far been ignored when assessing urban pluvial flood risk. In this paper, an urban flood hazard assessment framework using the latest 2.2 km resolution UK Climate Projections Local is proposed. Global warming induced changes in pluvial flood risks under RCP8.5 are projected, focusing on the impact of changing precipitation patterns and soil moisture dynamics on flood generation. Results indicate a strong increase in the frequency of occurrence of extreme floods, and the resultant future (2060–2080) annual flood volume is expected to increase up to 52.6% relative to 1980–2000 over a major UK urban region, and these patterns are likely to hold more generally elsewhere in the UK. Shifts to a later occurrence of extreme flooding is identified under global warming. Previous studies that have neglected soil moisture dynamics are unlikely to give accurate flood estimates.

Influence of reference transducer location on hearing protector attenuation metrics for impulse noise

The ANSI/ASA S12.42-2010 standard can be used to estimate the attenuation for impulsive noises between 130 and 170 decibels peak sound pressure level (dB pSPL). The ANSI/ASA S12.42 method uses a complex transfer function between the signal received in the ear of an acoustic test fixture (ATF) and a reference transducer. The reference transducer is at the same radial distance from the impulse source and at less than 30 degrees from the ATF angle. The reference transducer is specified as a pencil-type pressure (> 40.6 cm long). The maximum angle and the minimum pencil probe dimensions could be incompatible near the source, or may introduce artifacts or hazards. In this study, several hearing protectors were evaluated with two rifles (A-Bolt .300 Winchester Magnum and Colt AR-15 5.56 caliber), two ATFs (GRAS 45CB), and five transducers (four ¼” microphones and one surface mount microphone). The ATFs were on opposite sides of the gun at distances for field levels between 180- and 140-dB pSPL. For each location and rifle, S12.42 metrics were calculated for all 20 combinations of ATF ear and reference transducer. Results indicated that S12.42 metrics were minimally affected by the locations of the reference transducers.

Nonlinear dynamics of relative intensity noise transfer at fiber amplification and supercontinuum generation

Supercontinuum sources via femtosecond pumping in highly nonlinear photonic crystal fibers considerably impact scientific research and industrial applications. Herein, we investigate the complex transfer function of relative intensity noise in a broadband fiber supercontinuum source generated using an ytterbium-doped mode-locked laser. A designed intensity noise was artificially added to the system through the introduction of weak sinusoidal intensity modulation to the seed pulses. Owing to the influence of nonlinear gain dynamics and soliton dynamics during power amplification and spectral broadening, the transfer functions exhibit unique frequency and wavelength dependencies. Systematic measurements indicate that the seed transfer functions exhibit the characteristics of damped high-pass filters and saturate at low Fourier frequencies within the fiber amplifier. Moreover, supercontinuum broadening induces a nonlinear transformation of fluctuations, resulting in considerable amplification and negative correlation within the dispersion wave and soliton self-frequency shift regions. Clarifying the mechanism and bandwidth of this system is imperative to achieving low-noise supercontinuum generation because they provide insights into the nonlinear laser dynamics associated with broadband spectral broadening and noise transformation.

Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave

Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave

On Frequency/Time Invariance of Certain Temporal and Complex Transfer Functions for the One-Dimensional Interfacial Monochromatic Neutron Density Wave

Abstract Optimization of dynamical multibeam neutron cancer therapy has recently been shown to be possible via employment of the beam frequencies of neutron waves as a control variable. The concepts of transfer functions (TF), addressed in this paper, can be essential ingredients of such optimization. Accordingly, the paper studies the dynamics of a one-dimensional (1D) monochromatic neutron density wave generated by time modulation of a boundary neutron current. It is demonstrated that a certain temporal transfer function (TTF) of both parabolic (diffusion) and low frequency hyperbolic (P−1 transport) interfacial neutron density wave happens to be frequency noninvariant with a vibrating boundary neutron current. It is proved that, only at high frequencies, both parabolic and hyperbolic interfacial neutron waves turn out to have a fully frequency-invariant and time-invariant temporal transfer function relative to such a vibrating neutron beam at the boundary. The frequency response of an associated complex transfer function is studied and demonstrated to change behavior, from a lag compensator to a fixed gain amplifier, with changing the frequency, neutron absorption and employed theory for neutron diffusion. A highlight of this paper is its illustration that mere continuity of these transfer functions can be a reflection of the correctness of the transport theory employed for modeling the neutron density waves.

Phase-Corrected Proportional Resonant Control for Negative Sequence Current Elimination in High-Power Converters With Low Carrier Ratios

High-power converters operate at low carrier ratios (LCR) featuring significant digital delay, making it challenging to suppress negative sequence current stably under unbalanced grid voltage. In this paper, the worse amplification effect from negative sequence voltage to negative sequence current due to LCR under conventional proportional-integral (PI) control is first revealed and quantitatively explained with the complex transfer function. Furthermore, a phase-corrected proportional resonant (PR) controller is presented to suppress the amplification effect by the newly added pole and enhance the system stability by local phase correction (LPC). Meanwhile, a design scheme for phase correction angles is proposed to improve dynamics. Finally, simulation and experiments are provided to validate the negative sequence current elimination capability under various grid voltage sag depths as high as 100% at different carrier ratios as low as five, enhanced stability, and improved dynamic performance.

DETERMINATION OF THE DYNAMIC PARAMETERS OF THE MOBILE FIRE STATION OPERATOR IN THE FREQUENCY DOMAIN

Determination of the dynamic parameters of the operator of the mobile fire apparatus is based on the use of its amplitude-frequency and phase-frequency characteristics, the value of which is used at a priori set frequency. The value of these frequency characteristics of the operator of the mobile fire apparatus is used as initial data. Using the exponent and trigonometric form of the expression for the complex transfer function of the operator of the mobile fire apparatus, the functional dependence between its phase-frequency characteristic and dynamic parameters - the delay time and the operator's time constant - was obtained. This functional dependence is given in the form of two additive components, one of which is represented by a trigonometric function, the argument of which is the value of the phase-frequency characteristic of the operator and its delay time. The second additive component is a function of the time constant of the operator. The constructed functional dependence is used to determine the delay time of the operator of the mobile fire apparatus, provided that another dynamic parameter - the time constant - is determined using the amplitude-frequency characteristic of the operator and the normative value of its transmission coefficient. A graphical interpretation is given for the constructed functional dependence, which can be used as a component of the algorithm when determining the dynamic parameters of the operator of a mobile fire extinguisher. The algorithm for determining the dynamic parameters of the operator of a mobile fire installation is presented, which is presented in verbal form. The developed algorithm for determining the dynamic parameters of the operator of the mobile fire apparatus during its implementation involves the use of a graphical interpretation of the functional dependence between the delay time and the time constant of the operator of the mobile fire apparatus. The presented algorithm differs from the known ones by the simplicity of its implementation, which is ensured by reducing the number of a priori frequencies used to determine the values of the frequency characteristics by four times. An example of the implementation of the algorithm for determining the dynamic parameters of the operator of a mobile fire installation is given. Key words: operator, fire installation, dynamic parameters.

Effect of hearing protection attenuation on impulse insertion loss and kurtosis

Kurtosis (the fourth standardized moment of the sound pressure) has been used to assess the additional risk of hearing loss for complex or impulsive noise exposures. Murphy et al. [2012] reported the impulse peak insertion loss of five hearing protection devices (HPDs) for firearm impulse noise. Fackler et al. [2017] reported a spectral insertion loss for several HPDs assessed with firearm and shock tube impulse noise sources. Murphy [2019] previously reported the effect of five hearing protection devices on the kurtosis and insertion loss assessed with jackhammer noise. Unprotected Jackhammer noise exhibited kurtosis values between about 15 to 17, whereas protected exposures exhibited kurtosis between about 3 to 12. Anderson and Argo [2022] reported that insertion loss was unaffected by kurtosis level for seventeen HPDs measured on an acoustic test fixture under headphones. This paper will apply the complex transfer functions from Murphy et al. [2012] to the jackhammer noises measured by Murphy [2019]. The levels of the unoccluded noises transformed to the ear canal of the fixture will be compared to occluded jackhammer noises levels measured in the fixture.

Chromatic Dispersion Measurements of Single-Mode Fibers, Polarization-Maintaining Fibers, and Few-Mode Fibers Using a Frequency Domain Method

Chromatic dispersion is an important fiber attribute affecting transmission performance over optical fibers. Various chromatic dispersion measurement methods have been developed primarily for single-mode fibers. In the literature, measurement techniques were also developed to characterize few-mode fibers and multi-mode fibers. These methods are often subject to some limitations. In this paper, a simple and robust measurement method for chromatic dispersion measurement of single-mode fibers, polarization--maintaining fibers, and few-mode fibers is presented using a frequency domain instrument and a vector network analyzer. The method is applied to all three types of fibers through one measurement methodology uniformly. Using a vector network analyzer, the measurement instrument obtains the complex transfer function of fiber transmission. The inverse Fourier transform of the measured complex transfer function is used to determine the group delays for each mode of the fiber. Although the sampling is highly under-sampled for the whole fiber link, through proper treatment of the data, we can de-alias the signals and obtain accurate values of the group delays of each mode. By measuring the group delays over different wavelengths, the data can yield the chromatic dispersion of each mode over the wavelength window.

Application of spectral approximation to model the dynamic properties of wireless communication channels

This work is devoted to the application of approximation methods for modeling wireless radio communication channels. The rationale and prospects of the use of unmanned aerial vehicles as part of flying self-organizing networks for the transmission of high-speed information in the conditions of «smart cities» are demonstrated. The problem of using these networks is also referred, associated with the technical complexity of ensuring acceptable reliability and quality of wireless communication, associated with the multipath of signal propagation and a number of other factors. It is shown that in this aspect, the development of mathematical modeling methods of analyzing signals at the inputs of UAV radio receivers in order to evaluate their amplitude- phase transformations by a communication channel is of special significance. It has been established that the connection between the signals on the transmitting and receiving sides of an arbitrary wireless radio communication channel, assuming its linearity, can be uniquely determined by a complex transfer function in the frequency domain, which in practice is very complex and difficult to describe analytically. In this regard, an approach to its approximation by an equivalent model, described by fractional- rational functions of a complex variable, physically realized by mixed connections of various linear inertial and inertial links, is proposed, and for modeling dynamic characteristics, a numerical-a nalytical modeling technique based on the spectral method and piecewise linear approximation. A results of applying the proposed solutions are shown.

Active Cancellation of Periodic CM EMI at the Input of a Motor Inverter by Injecting Synthesized and Synchronized Signals (S3-AEF)

Active electromagnetic interferences (EMI) cancellation is a promising solution to reduce the size of passive filters. Power electronic systems may generate periodic disturbances if they are controlled by periodic signals in steady-state operation. Periodic disturbances can be represented by a set of sine waves, according to the Fourier theory, and can be suppressed by an appropriate set of cancelling sine waves injected into the system. Since bothersome effects, like delay times or complex transfer functions, can be compensated by individually selecting the appropriate amplitude and phase for each cancelling sine wave, high EMI reductions can be achieved in a wide frequency range. In this contribution, this cancellation method is applied to the common-mode EMI of a three-phase motor inverter in stationary operation with periodic control signals in the frequency range from 150 kHz to 30 MHz. Approximately 2.4 million harmonics are suppressed. The characteristics of the overall system are discussed and the challenges for the cancellation system are elaborated. A method for the synthesis of the cancellation signal is introduced. The design of the cancellation system is described, and its signal processing is presented. The outstanding performance is proven by reference measurements in a laboratory setup. Extensions for practical applications are discussed.

Spatial relationships between interaural differences in a room

The interaural ratio, as it occurs for a human head in a room, can be represented by a filter with a complex transfer function of the spatial location of the head. The log of this transfer function has real and imaginary parts, respectively, the interaural level difference (ILD) and the interaural phase difference (IPD). Because the filter is causal, the ILD and IPD spatial functions are Hilbert transforms of each other if the interaural filter is a minimum phase function of the head location. Interaural differences for a spherical “head” with tiny probe microphones, separated by a head diameter of 17.5 cm, were measured by Mr. Zane Crawford in an empty room having a volume of 63 $m∧3$ and a reverberation time of 0.4 s. The head was moved in increments of 2.54 cm over a two dimensional grid 102 cm by 23 cm. Measurements at 250 Hz showed that the ILD and IPD were almost perfectly related by Hilbert transforms. Measurements at 500 and 1000 Hz showed increasing deviations. Because a function is orthogonal to its Hilbert transform, the ideal ILD is orthogonal to the IPD. Therefore, at locations where the ILD is the most stable function of space, the IPD is the most unstable and vice versa.

Differential mode delay and modal bandwidth measurements of multimode fibers using frequency-domain method

• A frequency-domain method is developed to measure the DMD of multimode fibers. • Vector network analyzer is used to measure the complex transfer functions. • The time-domain output pulses can be calculated from CTF with proper procedures. • Frequency-domain method yields DMD results equivalent to the time domain method. • The frequency domain method can conduct DMD measurements at very low optical power. We report a frequency-domain method for measuring the differential mode delay (DMD) and bandwidth of multimode fibers (MMFs). Using a frequency domain instrument, vector network analyzer (VNA), the method measures the complex transfer functions (CTFs) of multimode fibers for a given set of launch conditions. As a result of the fiber length, which is long relative to sampling points used in VNA, the frequency sampling is under-sampled and the measured CTF is aliased. Aliased CTF behaves very differently from fully sampled CTF with dependence on the sampling frequency step. With proper procedures, the CTF can be transformed to local time frame centered around DMD into a modified CTF. The time-domain output pulses can be further recovered through an inverse Fourier transform. By recovering output pulses using complex transfer functions of a multimode fiber at controlled launch offsets, one can subsequently follow the same procedures of existing time domain methods to determine the effective modal bandwidth of the multimode fiber under test (FUT). As a result of the method, DMD and modal bandwidth measurements can be undertaken using frequency domain instruments rather than time domain instruments in a mathematically equivalent manner for multimode fibers. The measurement method utilizes CW light sources that are readily available in a wide range of wavelengths, thus providing greater flexibility for measuring the modal bandwidth of MMFs at different wavelengths, including WDM applications other than 850 nm. The very high sensitivity of the VNA allows the measurement at much lower optical power compared to the time domain instrument. Several measurements at 850 nm have been conducted using the frequency domain method and validated by comparison with the results from the time domain method. The method is suitable for measuring MMFs from a short length of a few hundred meters to a very long length close to 20 km. We have also measured an MMF at 910 nm using the method to demonstrate its flexibility in adopting different wavelengths.

Removal of transfer function effects from gear vibration signals under constant and variable speed conditions

Gear faults generally cause changes to the forcing functions of the system, which are usually hard to measure. Vibration is a common tool for gear condition monitoring, it being generated by a forcing function exciting responses through a transmission path from the excitation to the measurement point. The diagnostic information in the vibration measurements is often distorted by transfer function effects, in particular for local faults, such as cracks, where the waveform is important. In such cases, more direct diagnostic information can be extracted by removing the transfer function effects. However, a very limited amount of research has been carried out to reconstruct the time-domain waveforms of the forcing functions, except some making the assumption that the forcing functions are impulsive. A method was previously developed to identify and remove the transfer function effects from transmission error (TE) measurements at constant speeds to reconstruct the excitations, utilising a cepstrum-based operational modal analysis (OMA) method. In the current paper, this method is extended to vibration signals under constant and variable speed conditions. Since vibration has more complex transfer functions than TE, this paper establishes an additional pre-processing procedure, which removes the deterministic components in order to facilitate the OMA process. After removing the transfer function effects from measured vibration signals, the proposed technique reconstructs forcing functions that are much more clearly indicative of the faults at all speeds and which approximate the meshing forces at the gear teeth. The fault features are effectively enhanced and localised in the forcing functions, and the importance of phase modification to the reconstruction of forcing function waveforms is demonstrated. The technique was validated using vibration measurements obtained from a single stage spur gear box with a tooth root crack.

Parameters optimization and performance evaluation of multiple tuned mass dampers to mitigate the vortex-induced vibration of a long-span bridge

Vortex-induced vibration(VIV) is one of the primary dynamic problems of long-span bridges, which affects the safety and serviceability of bridges. The control and mitigation of VIV is a hotspot to researchers. Multiple tuned mass dampers(MTMD) consist of a set of tuned mass dampers(TMD) with varied frequencies and damping ratios, which is a common method for vibration control of structures. In this study, a concept of complex effective mass is proposed, which can entirely represent the dynamic effect of MTMD on bridges, and a derivative-based MTMD optimization process for VIV control of long-span bridges is presented. The VIV mitigation of a six-span continuous steel box-girder bridge is used to analyze the performance and mechanism of MTMD from the aspects of frequency domain and time domain. Optimal parameters of MTMD for suppressing VIV are obtained by the proposed algorithm. The results indicate that MTMD can significantly reduce the displacement amplitude of the beam due to VIV, and the performance of MTMD is better than that of single tuned mass damper(STMD) with the same mass ratio. The optimal performance of MTMD is independent of the mass distribution of the sub-TMDs. Moreover, the damping ratio of MTMD is much lower than that of STMD, but it can still help the vibration of the primary structure to decay faster. Complex mode theory and transfer function theory are used to explain this phenomenon. It indicates that the performance of MTMD does not depend on its damping ratio but is due to the phase interference between complex modes, and a one-way energy barrier between the bridge deck and MTMD can be formed, which prevents the transfer of vibration energy from MTMD to the primary structure after unloading. Finally, the stroke of MTMD in the control of long-span bridge VIV is analyzed, and a simplified formula is proposed.

Exploration of new analytical correlations as an alternative to the Kramers-Kronig transforms for the assessment of impedance spectroscopy data

• Alternative method to detect errors in EIS spectra. • Overcome of some practical issues for assessment of simple spectra. • Elucidation of analytical correlations between magnitude and phase. New analytical correlations between impedance magnitude and phase are developed and presented. These correlations are used for the assessment of impedance spectroscopy data. As correlations are obtained, they can be calculated point to point at each frequency of the spectra with no need to establish explicit premises related to stability, linearity or finite limits for their derivation. Their use is simpler than that based on the direct evaluation of the Kramers-Kroning transforms or alternative methods. An example of their derivation from basic equations involving complex numbers is described. They were obtained by looking for an explanation of the empirical fact that the slope of the Bode-Magnitude diagram vs frequency resembles the shape of the corresponding Bode-Phase diagram. Unlike the Kramers-Kronig transform, these new correlations can also be directly applied to test spectra with highly predominant capacitive or inductive responses or even incomplete loops. Their analytical expressions are exact for simple ideal elements and circuits, including the Warburg diffusion element. These correlations were tested with simulated spectra altered with known random error distributions, and they were able to detect the random distribution and the error level for simple spectra when the errors were > 0.5%. For more sophisticated spectra, the minimum error that can be detected without interference of the deviations due to the proper algorithm are around 2.5%. No exact correlation was found for a constant phase element (CPE), but a close empirical approximation was obtained for a single CPE. It is necessary to improve this approximation when a CPE is combined with some other elements because of detected deviations. In addition, it was found that in a first approach the algorithm does not detect non-linear behavior on a simple experimental circuit, but the test gave insights of how to detect it. On the contrary, it is well suited for detection of system stability issues. Examples of their application to actual experimental spectra, high capacitive or with several loops, are presented and the limitations discussed. More work and exhaustive tests are necessary to improve the method and stablish its real limitations, but its use for assessment of simple spectra at certain error level can already be done. Given that the derivation of the new correlations is only based on its complex number nature, this study concludes that the magnitude and phase of any complex number or 2D vector are not independent, and it is expected that similar correlations can be applied to any frequency-dependent complex variable, vector or transfer function, such as those used in optics or rheology.

Dynamics of Time-Delayed Optoelectronic Oscillators With Nonlinear Amplifiers and Its Potential Application to Random Numbers Generation

Time-delayed dynamical systems generally feature smooth nonlinear transfer functions in the feedback loop, such as polynomial or sinusoidal functions. As a consequence, the complexity of their dynamical behavior mainly originates from the time-delay. In this paper, we explore the opposite case where the nonlinear transfer function is complex ( cos <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (sinh)), and therefore, non-smooth. We perform a bifurcation analysis of the system, and evidence that this novel type of time-delayed system can display a chaotic behavior characterized by positive maximum Lyapunov exponent and quasi-maximal entropy. The high entropy behavior of the system combined with post-processing are used to generate random numbers for small values of the feedback gain with an overall bit rate up to 1.478 Gb/s. Our theoretical results are in excellent agreement with experimental measurements, performed with an optoelectronic oscillator involving a complex transfer function designed ad hoc.

Primary calibration of mechanical sensors with digital output for dynamic applications

This article tackles the challenge of the dynamic calibration of modern sensors with integrated data sampling and purely digital output for the measurement of mechanical quantities like acceleration, angular velocity, force, pressure, or torque. Based on the established calibration methods using sine excitation, it describes an extension of the established methods and devices that yields primary calibration results for the magnitude and phase of the complex transfer function. The system is demonstrated with a focus on primary accelerometer calibrations but can easily be transferred to the other mechanical quantities. Furthermore, it is shown that the method can be used to investigate the quality and characteristics of the timing for the internal sampling of such digital output sensors. Thus, it is able to gain crucial information for any subsequent phase-related measurements with such sensors.